Jackknife empirical likelihood inference with regression imputation and survey data

We propose jackknife empirical likelihood (EL) methods for constructing confidence intervals of mean with regression imputation that allows ignorable or nonignorable missingness. The confidence interval is constructed based on the adjusted jackknife pseudo-values (Rao and Shao, 1992). The proposed EL ratios evaluated at the true value converge to the standard chi-square distribution under both missing mechanisms for simple random sampling. Thus the EL can be applied to construct a Wilks type confidence interval without any secondary estimation. We then extend the proposed method to accommodate Poisson sampling design in survey sampling. The proposed methods are compared with some existing methods in simulation studies. We also apply the proposed method to an Italy household income panel survey data set.